Question

Line joining the points (0, 3) and (5, 2) is a tangent to the curve y = ax/(1+x), then a=?

Answer 1

Answer:

How do I determine C, so that the straight line joining (0,3) and (5,2) is tangent to the curve y = c/(x+1) ?

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Student Answers

TONYS538 | STUDENT

The value of c is required such that the line joining the points (0,3) and (5,2) is tangent to the curve y = c/(x+1).

The equation of the line joining (0,3) and (5,2) is given by (y - 3)/(x - 0) = (2-3)/(5 - 0)

or (y - 3)*5 = -1*x

or x = 15 - 5y

Now this line is a tangent to y = c/(x +1)

y = c/(x+1)

y*(x + 1) = c

Replace x by 15 - 5y

y*(15 - 5y + 1) = c

16y - 5y^2 - c = 0

As the line is tangent to the curve, 16y - 5y^2 - c = 0 has only one solution. An equation ax^2 + bx + c = 0 has one root when b^2 = 4ac. For the equation derived this is the case when 16^2 - (4*-5*-c) = 0

c = 256/20 = 12.8

The required value of c is 12.8